Quote:
Originally Posted by Weevil99
Good point. Card removal effects could skew the results somewhat. The new numbers (for pocket pairs 9 or smaller):
673 flops seen
58 sets or better
0.118 (unchanged, obviously)
That improved things quite a bit. Now I'm only getting 2.6 standard deviations below expectation. Actually, that almost looks like too much of an improvement. I wouldn't have expected card removal effects to be worth a full standard deviation, would you?
Quote:
Originally Posted by AaronT
I couldn't tell if the question was directed generally or at me in particular. But I don't think that:
A) There's enough information to answer the question. It depends on the particular game you're playing - big difference here between heads up/no-limit/high stakes vs low stakes/full ring/limit, the behavior of your opponents, and your play - or at least how your opponents perceive your play.
B) I'm qualified to answer the question even if there was enough information.
Oh. Well, you're as ignorant as I am, then. That's no good. When you jumped into a question addressed to Pyro, I figured you were a statistics guy, too.
A) If any of the things you mention here have this large of an effect, then every book on poker is very wrong about the odds. If the probability of flopping a set differs wildly from 11.8% depending on whether you're playing full ring or heads up, low stakes or high stakes, how your opponents behave, and your own table image...then I think you've uncovered some major new poker theory.
B) Yeah, I'm not, either, but I can speculate with the best of them, which is always fun until a mathematician comes in and poops the party. But that's actually what I was wanting, here.
To find the standard deviation for flopping a set, I used the formula:
SQRT(npq)
where
n = number of trials
p = probability of flopping a set
q = 1-p
Not being a mathematician, I had to find that formula on the internet. I already knew you could calculate it if you have all the data points (by finding the mean, individually finding the differences, etc.), but I was a little surprised that simply knowing the number of trials and the probability of success allowed one to calculate the standard deviation for a data set. There has to be an assumption about the shape of the data, here, and I'm guessing the assumption in this case is that the underlying distribution is normal.
My question is...okay, I can't really articulate a specific question. I'd just like to read some educated speculation about why narrowing the data from all pocket pairs to just 9s and under had such a big effect. Sample size issue? Something to do with an erroneous assumption about the distribution? Card removal effects? Just a random outlier in the universe of poker results?
And is it even that much of an anomaly? 3.7 and 2.6 standard deviations are pretty far out there, and so is the difference between them, but with the number of people who play poker, we should expect quite a few outliers like that and several that are much worse.
Also, it would be interesting to know if the set-flopping results in Indy's huge data base form a normal distribution or something else.
Last edited by Weevil99; 10-13-2009 at 06:11 AM.